Empirical probability

From the calculated building damage versus response relationship and the empirical probability of serious injury or fatality versus damage relationship discussed above, the relationship between explosion overpressure (or other effects) and probability of serious injury or fatality may be constructed in a manner that accounts for the detailed structural characteristics of plant buildings. The steps involved are similar to risk screening (Chapter 4), with the addition of detailed quantitative structural evaluation of plant buildings and detailed quantitative frequency assessment as described in the next section. 

We calculate the empirical frequency that Drug C is selected as least safe based on Safel probabilities or log odds ratios for a Bayesian or frequentist model, respectively, over 1000 simulations. We call this the empirical probability of correct decision (i.e., that Drug C is the worst drug). Tables 12.2 and 12.3 present the probability of correct decision with various parameter... 

Since so many subjective judgments are necessary in applying what are otherwise sound statistical quantification systems, I believe that, except when statistical concepts can be applied to the known such as the face markings of dice, or when empirical probability evidence has been produced, all quantitative risk analyses are really qualitative risk analyses. 

Equation (6) has also been verified by a Monte Carlo simulation. Thus, forS = 300, Cf = —100, Ps = 0.3, pf = 0.7 and 12 opportunity bets, equation (6) gives 0.253 for the probability of a net loss. This result has been confirmed by an empirical probability of 0.253, obtained on the basis of 1000000 simulation trials. 

There are three types of probability which are likely to be encountered a priori probability, empirical probability and conditional probability. 

Empirical probabilities are also used in working out certain accident probabilities. For example, if there have been ten accidents during one hundred shifts, then it is possible to express the probability of an accident on a given shift as... 

However, great care should be taken when using empirical probabilities in this context since it is theoretically possible to have 101 accidents in 100 shifts which would give a probability of... 

Once the physico-chemical basis of secondary structure packing is determined, and once the local interactive forces that give rise to secondary structure are known, it vrill be possible to predict both the folding pathway and the final stable conformation of a protein from its amino-add sequence. There are three approaches to these problems, (a) One can correlate sequence and structure using data from as many proteins as possible and derive empirical probabilities for any particular sequence-forming secondary structure, (b) One can derive semi-empirical energy functions for amino-add sequences based on allowed conformation around the... 

Empirical Probability When many possible outcomes can result, including a desired outcome, the probability of occurrence of such outcomes is referred to as empirical and requires statistical evaluation to determine the likelihood of expected results based upon past performance. 

We can focus on the effect of epistemic uncertainty only by calculating the mean farm availability averaged over the whole early life from the inner-loop iterations of the model. Figure 8 shows the empirical probability distribution of this mean. 

Eor each path , two quantities are considered for the pohcy assessment the life cycle duration (time until preventive replacement or failure) and the type of replacement (preventive or corrective). In the case of simulated data, it is possible to derive the empirical the mean life cycle duration by dass t and the empirical probability of failure P/. 

The simulation has been repeated for 500 path sets. The empirical probability of failure p and the empirical mean life cycle duration by class T are given in Table 2(a) and (b) for situation 1, with simulations done between / = 0 and / = 100. Similar results are given in Table 3 for situation 2 with simulations done between / = 0 and /= 100, and in Table 4 for situation 2 with simulations done between / = 0 and = 60. 

The distribution of laser points in the image is discrete and it is difficult to locate points directly with a maximum density around. The mean shift presented by Comaniciu and Meer [COM 99] is a powerful non-parametric algorithm that allows us to find the local maximum of a function of the underlying density. It estimates the feature space as an empirical probability density function. For each data point, the mean shift defines a window and calculates the average of data within the window. Then it moves the center of the window to the average in the direction of the... 

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